# What is a general solution to the differential equation #dy/dx=x^3/y^2#?

Integrate both sides:

Using the typical integration power rule:

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The general solution to the differential equation ( \frac{dy}{dx} = \frac{x^3}{y^2} ) can be found by separating variables and integrating both sides.

- Separate variables: ( y^2 , dy = x^3 , dx ).
- Integrate both sides: [ \int y^2 , dy = \int x^3 , dx ]

After integration, we have: [ \frac{1}{3}y^3 = \frac{1}{4}x^4 + C ]

Where ( C ) is the constant of integration.

Thus, the general solution to the given differential equation is: [ y^3 = \frac{4}{3}x^4 + C ]

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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